PD Presentation: |
X6172 X12,3,13,4 X20,13,5,14 X14,7,15,8 X8,19,9,20 X16,10,17,9 X18,16,19,15 X10,18,11,17 X2536 X4,11,1,12 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 2 |
In[3]:= | Show[DrawMorseLink[Link[10, Alternating, 26]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 26]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[20, 13, 5, 14], X[14, 7, 15, 8],
> X[8, 19, 9, 20], X[16, 10, 17, 9], X[18, 16, 19, 15], X[10, 18, 11, 17],
> X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {9, -1, 4, -5, 6, -8, 10, -2, 3, -4, 7, -6, 8, -7,
> 5, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 3 6 10 12 15 13 11
q - ----- + ----- - ---- + ---- - ---- + ---- - ------- + 8 Sqrt[q] -
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q
3/2 5/2
> 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 -22 -20 2 2 4 5 -8 2 -4 3 2
2 - q - q + q - --- + --- + --- + --- + q + -- + q - -- - 3 q +
18 16 14 10 6 2
q q q q q q
6 8
> 2 q - q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 26]][a, z] |
Out[8]= | 3 5 7 3
a 4 a 4 a a 3 5 7 z 3 3
- - ---- + ---- - -- + 2 a z - 9 a z + 6 a z - a z + -- - 6 a z +
z z z z a
5 3 5 3 5
> 3 a z - a z - 2 a z |
In[9]:= | Kauffman[Link[10, Alternating, 26]][a, z] |
Out[9]= | 3 5 7
2 4 6 8 a 4 a 4 a a 3
1 + 4 a + 7 a + 4 a + a - - - ---- - ---- - -- + 3 a z + 15 a z +
z z z z
3
5 7 2 2 2 4 2 6 2 8 2 2 z
> 16 a z + 4 a z - 3 z - 14 a z - 21 a z - 13 a z - 3 a z + ---- -
a
4
3 3 3 5 3 7 3 4 z 2 4 4 4
> 7 a z - 34 a z - 34 a z - 9 a z + 9 z - -- + 20 a z + 16 a z +
2
a
5
6 4 8 4 4 z 5 3 5 5 5 7 5 6
> 9 a z + 3 a z - ---- + 12 a z + 41 a z + 34 a z + 9 a z - 8 z -
a
2 6 4 6 6 6 8 6 7 3 7 5 7
> 4 a z + 8 a z + 3 a z - a z - 9 a z - 16 a z - 10 a z -
7 7 2 8 4 8 6 8 3 9 5 9
> 3 a z - 5 a z - 8 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 6 1 2 1 4 2 6 5 7
6 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
2 16 7 14 6 12 6 12 5 10 5 10 4 8 4 8 3
q q t q t q t q t q t q t q t q t
5 8 7 5 8 2 2 2 4 2 6 3
> ----- + ----- + ----- + ---- + ---- + 3 t + 5 q t + q t + 3 q t + q t
6 3 6 2 4 2 4 2
q t q t q t q t q t |